Laura Jesson (Johnson), a suburban housewife in a dull but affectionate marriage, tells her story in the first person while at home with her husband, imagining that she is confessing her affair to him.

Conventional Laura, as with most women of her class at that time, goes to the nearby town of Milford once a week for shopping and to the cinema for a matinée. Returning home from one of her weekly excursions, at the station she gets a piece of grit in her eye which is removed by another passenger, a doctor called Alec Harvey (Howard). Both are in their thirties; each is married, with two children. The doctor is a general practitioner who also works one day a week as a consultant at the local hospital, but his passion is for preventive medicine, such as addressing the causes of respiratory illness in miners.

Enjoying each other's company, the two arrange to meet again. They are soon troubled to find their innocent and casual relationship quickly developing into love.
For a while, they meet furtively, constantly fearing chance meetings with friends. After several meetings, they go to a room belonging to a friend and fellow doctor of Alec's, Stephen (Valentine Dyall). But they are interrupted by Stephen's unexpected return. This brings home the fact that a future together is impossible and, wishing not to hurt their families, they agree to part. Alec has been offered a job in Johannesburg, South Africa, where his brother lives.

Their final meeting is at the railway station refreshment room which we see for the second time with the poignant perspective of their story. As they await a sad and final parting, Dolly Messiter, a talkative acquaintance of Laura, invites herself to join them and is soon chattering away, totally oblivious to the couple's inner misery.

As they realise that they have been robbed of the chance for a final goodbye, Alec's train arrives. With Dolly still chattering, Alec departs with a last look at Laura but without the passionate farewell for which they both long. After shaking Messiter's hand, he lightly squeezes Laura on the shoulder and leaves. Laura waits for a moment, anxiously hoping that Alec will walk back into the refreshment room; he does not. As the train is heard pulling away, Laura suddenly dashes out onto the platform. The lights of a passing express train flash across her face as she conquers her impulse to commit suicide; she then returns home to her family.
In the final scene of the film, which does not appear in the original Coward play, Laura's bland but kind husband Fred suddenly shows that he has not been completely oblivious to her distress in the past weeks, and takes her in his arms.